This section includes limits on on-shell production of gravitons in collider and astrophysical processes. Bounds quoted are on $\mathit R$, the assumed common radius of the flat extra dimensions, for $\delta $ = 2 extra dimensions. Studies often quote bounds in terms of derived parameter; experiments are actually sensitive to the masses of the KK gravitons: $\mathit m_{\vec n}$ = $\vert \vec n\vert /\mathit R$. See the Review on ``Extra Dimensions'' for details. Bounds are given in $\mu $m for $\delta $ = 2.

1AABOUD 2016D search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ , using 3.2 fb${}^{-1}$ of data at $\sqrt {s }$ = 13 TeV to place lower limits on ${{\mathit M}_{{D}}}$ for two to six extra dimensions (see their Table X), from which this bound on ${{\mathit R}}$ is derived.

2HANNESTAD 2003 obtain a limit on $\mathit R$ from the heating of old neutron stars by the surrounding cloud of trapped KK gravitons. Limits for all $\delta {}\leq{}$7 are given in their Tables$~$V and VI. These limits supersede those in HANNESTAD 2002 .

4AABOUD 2016F search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ , using 3.2 fb${}^{-1}$ of data at $\sqrt {s }$ = 13 TeV to place limits on ${{\mathit M}_{{D}}}$ for two to six extra dimensions (see their Figure 9), from which this bound on ${{\mathit R}}$ is derived.

6AAD 2015BH search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ , using 20.3 fb${}^{-1}$ of data at $\sqrt {s }$ = 8 TeV to place bounds on ${{\mathit M}_{{D}}}$ for two to six extra dimensions, from which this bound on ${{\mathit R}}$ is derived. See their Figure 9 for bounds on all ${{\mathit \delta}}{}\leq{}$ 6.

8KHACHATRYAN 2015AL search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ , using 19.7 fb${}^{-1}$ of data at $\sqrt {s }$ = 8 TeV to place bounds on ${{\mathit M}_{{D}}}$ for two to six extra dimensions (see their Table 7), from which this bound on ${{\mathit R}}$ is derived.

9AAD 2013AD search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ , using 4.7 fb${}^{-1}$ of data at $\sqrt {s }$ = 7 TeV to place bounds on ${{\mathit M}_{{D}}}$ for two to six extra dimensions, from which this bound on ${{\mathit R}}$ is derived. See their Table 8 for bounds on all ${{\mathit \delta}}{}\leq{}$ 6.

10AAD 2013C search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ , using 4.6 fb${}^{-1}$ of data at $\sqrt {s }$ = 7 TeV to place bounds on ${{\mathit M}_{{D}}}$ for two to six extra dimensions, from which this bound on ${{\mathit R}}$ is derived.

11AAD 2013D search for the dijet decay of quantum black holes in 4.8 fb${}^{-1}$ of data produced in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV to place bounds on ${{\mathit M}_{{D}}}$ for two to seven extra dimensions, from which these bounds on ${{\mathit R}}$ are derived. Limits on ${{\mathit M}_{{D}}}$ for all $\delta $ ${}\leq{}$ 7 are given in their Table 3.

12AJELLO 2012 obtain a limit on ${{\mathit R}}$ from the gamma-ray emission of point ${{\mathit \gamma}}$ sources that arise from the photon decay of KK gravitons which are gravitationally bound around neutron stars. Limits for all ${{\mathit \delta}}{}\leq{}$ 7 are given in their Table 7.

13CHATRCHYAN 2012AP search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ , using 5.0 fb${}^{-1}$ of data at $\sqrt {s }$ = 7 TeV to place bounds on ${{\mathit M}_{{D}}}$ for two to six extra dimensions, from which this bound on ${{\mathit R}}$ is derived. See their Table 7 for bounds on all ${{\mathit \delta}}{}\leq{}$ 6.

14AAD 2011S search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ , using 33 pb${}^{-1}$ of data at $\sqrt {s }$ = 7 TeV, to place bounds on ${{\mathit M}_{{D}}}$ for two to four extra dimensions, from which these bounds on ${{\mathit R}}$ are derived. See their Table 3 for bounds on all ${{\mathit \delta}}{}\leq{}$ 4.

15CHATRCHYAN 2011U search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ , using 36 pb${}^{-1}$ of data at $\sqrt {s }$ = 7 TeV, to place bounds on ${{\mathit M}_{{D}}}$ for two to six extra dimensions, from which these bounds on ${{\mathit R}}$ are derived. See their Table 3 for bounds on all ${{\mathit \delta}}{}\leq{}$ 6.

16AALTONEN 2008AC search for ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ and ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ at $\sqrt {s }$ = 1.96 TeV with 2.0 fb${}^{-1}$ and 1.1 fb${}^{-1}$ respectively, in order to place bounds on the fundamental scale and size of the extra dimensions. See their Table III for limits on all $\delta {}\leq{}$ 6.

17ABAZOV 2008S search for ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ , using 1 fb${}^{-1}$ of data at $\sqrt {s }$ = 1.96 TeV to place bounds on ${{\mathit M}_{{D}}}$ for two to eight extra dimensions, from which these bounds on $\mathit R$ are derived. See their paper for intermediate values of $\delta $.

18DAS 2008 obtain a limit on $\mathit R$ from Kaluza-Klein graviton cooling of SN1987A due to plasmon-plasmon annihilation.

20ABDALLAH 2005B search for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ at $\sqrt {s }$ = $180 - 209$~GeV to place bounds on the size of extra dimensions and the fundamental scale. Limits for all $\delta $ ${}\leq{}$ 6 are given in their Table~6. These limits supersede those in ABREU 2000Z.

21ACHARD 2004E search for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ at $\sqrt {s }$ = $189 - 209$~GeV to place bounds on the size of extra dimensions and the fundamental scale. See their Table~8 for limits with $\delta $ ${}\leq{}$ 8. These limits supersede those in ACCIARRI 1999R.

22ACOSTA 2004C search for ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ at $\sqrt {s }$ = 1.8~TeV to place bounds on the size of extra dimensions and the fundamental scale. See their paper for bounds on $\delta $~=~4,~6.

23CASSE 2004 obtain a limit on $\mathit R$ from the gamma-ray emission of point ${{\mathit \gamma}}$ sources that arises from the photon decay of gravitons around newly born neutron stars, applying the technique of HANNESTAD 2003 to neutron stars in the galactic bulge. Limits for all $\delta {}\leq{}$7 are given in their Table~I.

24ABAZOV 2003 search for ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ at $\sqrt {\mathit s }$=1.8 TeV to place bounds on $\mathit M_{\mathit D}$ for 2 to 7 extra dimensions, from which these bounds on $\mathit R$ are derived. See their paper for bounds on intermediate values of $\delta $. We quote results without the approximate NLO scaling introduced in the paper.

25HANNESTAD 2003 obtain a limit on $\mathit R$ from graviton cooling of supernova SN1987a. Limits for all $\delta {}\leq{}$7 are given in their Tables$~$V and VI.

26HANNESTAD 2003 obtain a limit on $\mathit R$ from gravitons emitted in supernovae and which subsequently decay, contaminating the diffuse cosmic$~{{\mathit \gamma}}$ background. Limits for all $\delta {}\leq{}$7 are given in their Tables$~$V and VI. These limits supersede those in HANNESTAD 2002 .

27HANNESTAD 2003 obtain a limit on $\mathit R$ from gravitons emitted in two recent supernovae and which subsequently decay, creating point$~{{\mathit \gamma}}$ sources. Limits for all $\delta {}\leq{}$7 are given in their Tables$~$V and VI. These limits are corrected in the published erratum.

28HEISTER 2003C use the process ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ at $\sqrt {\mathit s }$ = $189 - 209$ GeV to place bounds on the size of extra dimensions and the scale of gravity. See their Table$~$4 for limits with $\delta {}\leq{}$6 for derived limits on $\mathit M_{\mathit D}$.

29FAIRBAIRN 2001 obtains bounds on $\mathit R$ from over production of KK gravitons in the early universe. Bounds are quoted in paper in terms of fundamental scale of gravity. Bounds depend strongly on temperature of QCD phase transition and range from $\mathit R<0.13~\mu $m to $0.001~\mu $m for $\delta $=2; bounds for $\delta $=3,4 can be derived from Table$~$1 in the paper.

Search for New Phenomena with the Monojet and Missing Transverse Momentum Signature using the ATLAS Detector in $\sqrt {s }$ = 7 TeV Proton$−$Proton Collisions

CHATRCHYAN

2011U

PRL 107 201804

Search for New Physics with a Monojet and Missing Transverse Energy in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV

AALTONEN

2008AC

PRL 101 181602

Search for Large Extra Dimensions in Final States Containing one Photon or Jet and Large Missing Transverse Energy Produced in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96$~$TeV

ABAZOV

2008S

PRL 101 011601

Search for Large Extra Dimensions via Single Photon Plus Missing Energy Final States at $\sqrt {s }$ = 1.96 TeV

DAS

2008

PR D78 063011

Plasmon Annihilation into Kaluza-Klein Gravitons: New Astrophysical Constraints on Large Extra Dimensions?

ABULENCIA,A

2006

PRL 97 171802

Search for Large Extra Dimensions in the Production of Jets and Missing Transverse Energy in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV